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4th International ICST Workshop on Tools for solving Structured Markov Chains

Research Article

Approximation of discrete-time polling systems via structured Markov chains

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BibTeX Plain Text
  • @INPROCEEDINGS{10.4108/ICST.VALUETOOLS2009.7667,
        author={P.  Beekhuizen and J.A.C.  Resing},
        title={Approximation of discrete-time polling systems via structured Markov chains},
        proceedings={4th International ICST Workshop on Tools for solving Structured Markov Chains},
        publisher={ACM},
        proceedings_a={SMCTOOLS},
        year={2010},
        month={5},
        keywords={Polling Bernoulli scheduling Markovian routing Networks on chips},
        doi={10.4108/ICST.VALUETOOLS2009.7667}
    }
    
  • P. Beekhuizen
    J.A.C. Resing
    Year: 2010
    Approximation of discrete-time polling systems via structured Markov chains
    SMCTOOLS
    ICST
    DOI: 10.4108/ICST.VALUETOOLS2009.7667
P. Beekhuizen1,2,*, J.A.C. Resing3,*
  • 1: Philips Research, Eindhoven, The Netherlands
  • 2: EURANDOM, Eindhoven University of Technology
  • 3: Eindhoven University of Technology, Department of Mathematics and Computer Science, Eindhoven, The Netherlands.
*Contact email: beekhuizen@eurandom.tue.nl, resing@win.tue.nl

Abstract

We devise an approximation of the marginal queue length distribution in discrete-time polling systems with batch arrivals and fixed packet sizes. The polling server uses the Bernoulli service discipline and Markovian routing. The 1- limited and exhaustive service disciplines are special cases of the Bernoulli service discipline, and traditional cyclic routing is a special case of Markovian routing. The key step of our approximation is the translation of the polling system to a structured Markov chain, while truncating all but one queue. Numerical experiments show that the approximation is very accurate in general. Our study is motivated by networks on chips with multiple masters (e.g., processors) sharing a single slave (e.g., memory).

Keywords
Polling Bernoulli scheduling Markovian routing Networks on chips
Published
2010-05-16
Publisher
ACM
Modified
2010-05-16
http://dx.doi.org/10.4108/ICST.VALUETOOLS2009.7667
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